Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x+8y &= 7 \\ 2x+3y &= -7\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $3y = -2x-7$ Divide both sides by $3$ to isolate $y$ $y = {-\dfrac{2}{3}x - \dfrac{7}{3}}$ Substitute this expression for $y$ in the first equation. $-2x+8({-\dfrac{2}{3}x - \dfrac{7}{3}}) = 7$ $-2x - \dfrac{16}{3}x - \dfrac{56}{3} = 7$ Simplify by combining terms, then solve for $x$ $-\dfrac{22}{3}x - \dfrac{56}{3} = 7$ $-\dfrac{22}{3}x = \dfrac{77}{3}$ $x = -\dfrac{7}{2}$ Substitute $-\dfrac{7}{2}$ for $x$ back into the top equation. $-2( -\dfrac{7}{2})+8y = 7$ $7+8y = 7$ $8y = 0$ $y = 0$ The solution is $\enspace x = -\dfrac{7}{2}, \enspace y = 0$.